Define f:R--->R as follows:

f(x)=x-[x] if [x] is even

f(x)=x-[x+1] if [x] is odd

Determine the points where f has a limit and justify

Not quite sure how to get started...

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- Nov 5th 2008, 11:11 AMkathrynmathDetermine where f has a limit
Define f:R--->R as follows:

f(x)=x-[x] if [x] is even

f(x)=x-[x+1] if [x] is odd

Determine the points where f has a limit and justify

Not quite sure how to get started... - Nov 5th 2008, 12:04 PMPlato
- Nov 5th 2008, 02:11 PMkathrynmath
So, I just use the graph and see where ther is a limit? Then I can use a formula to justify that these are correct limits?

- Nov 5th 2008, 02:43 PMPlato
- Nov 5th 2008, 05:55 PMkathrynmath
Ok, so there is a limit everywhere except for the integers. how would I justify using a theorem. Lim(F(x)+G(x))=LimF(x)+LimG(x)?

- Nov 5th 2008, 08:07 PMkathrynmath
- Nov 12th 2008, 09:35 PMkathrynmath
- Nov 15th 2008, 10:36 AMkathrynmath
Limit only at the even numbers?

if 1<x<2, [x]=1 Then f(x)=x-2. The limit=0

If 2<x<3 [x]=2 Then f(x)=x-2 The limit =0

a-1<x<a where a is an odd number. [x]=a-1. Then f(x)=x-(a-1). Limit as x goes to a=1

a<x<a+1 where a is an odd number. [x]=a. Then f(x)=x-(a-1+1). Limit as x goes to a= 0

a-1<x<a where a is an even number. [x]=a-1. Then f(x)=x-(a-1+1). Limit=0

a<x<a+1 where a is an even number. [x]=a. Then f(x)=x-a. Limit = 0

So the limit exists for even numbers, it seems. - Nov 15th 2008, 11:13 AMkathrynmath